Dressing chain equations associated to difference soliton systems

TL;DR

This paper derives dressing chain equations linked to difference soliton systems, revealing their role in generating solutions through Darboux transformations and illustrating with Hirota and Nahm equations.

Contribution

It introduces a novel derivation of dressing chain equations for difference soliton systems and explores their symmetry properties via Darboux transformations.

Findings

Dressing chain equations are derived for difference soliton systems.

Solutions are generated through covariant Darboux transformations.

Examples include Hirota and Nahm equations.

Abstract

The dressing chain equations for factorizing operators of a spectral problem are derived. The chain equations itselves yield nonlinear systems which closure generates solutions of the equations as well as of the nonlinear system if both operators of the correspondent Hirota bilinearization are covariant with respect to Darboux transformation which hence defines a symmetry of the nonlinear system as well as of these closed chains. Examples of Hirota and Nahm equations are specified.